Denq2007-10-29 15:05:58

Hi,

I also work on drop impact with solid as well as fluid surface.I would

appreciate if someone can share numerical models or provide some advice.

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Sucklinp2007-10-29 15:06:29

Sorry for the delay in replying. I have been away for a while.

Oh no… I just found it funny (:#

In principle, both could do the job, but the finite element method can

capture moving interfaces far more easily than the finite difference

method. Capturing the free surface and contact line motion accuractely

is crucial in a drop spreading problem, where capillarity is a crucial

effect that has to be modelled.

With the finite difference method you start with a fixed grid

(Cartesian probably, but see my comments later), and discretise the

spatial derivative operators such as div and grad etc on the grid. If

your interfaces lie along grid lines and does not move then this works

very well. If your interface doesn’t lie along the grid lines and is

not fixed like in our problem then what? a) The biasing of the

discretised versions of the derivative operators becomes far more

complicated. b) How do you handle the fact that the number of unknowns

in your solution will be changing at each time step etc. c) How do you

know where your interface actually is? For example, if the contact

line position that you are solving for lies between two grid points,

then where exactly is it, and how do you accurately apply boundary

conditions there?

There are some ways of trying to overcome these problems, like using

body fitted coordinates so that the mesh remains fixed with respect to

the drop. However, in practise this method only works for very small

deformations and is not suitable for drop impact problems. If you are

going to go down the finite difference route, then I suggest you do

something like the following: Use a coordinate system which is centred

on and moves with the contact line, which is polar local to the

contact line, and Cartesian far away from it. Such coordinate systems

exist (I know this because I base my FE grid on one), and this will at

least mean that you capture the interface accurately where it matters

most: Near the contact line. Be warned though, that deriving the

discretised form of the operators will be so complicated as to be

virtually impossible to get correct. Remember that in order to

calculate the curvature in the normal stress condition you will need

to accurately calculate second derivates of free surface shape.

With the finite element method on the other hand, you split the domain

up into regions with shape of your own choosing, and approximate the

functional form of the solution over each of those regions rather than

discretising derivative operators. Typically the solution is

approximated by quadratic and linear forms. You can then choose the

shape and position of the elements such that the interface is

accurately captured. The mesh will have to move with time as the

interface moves however, and become quite deformed during impact, so

you would have to think carefully about how to handle this. One way is

to use a Lagrangian formulation from the start, another to use an

Eularian formulation but to map the positions of the nodes of the

elements with the flow. I would argue against using either of these

methods, since the fluid flow inside the drop is so complicated that

the mesh deteriorates very quickly. I suggest using director based

method or some other critereon. A hint/tip for you is that since you

are dealing with an integral form of the equations you can do

integration by parts on the curvature and only every have to calculate

first derivatives of free surface shape.

Hope this helps!

Very interesting. Prof Veldman obviously has a HUGE amount of

computing power to hand. No mention of the model used for spreading

though. I am always curious when people don’t mention how they have

overcome the problems with the fact that there is no solution to the

classical fluid mechanical model. I’d be interested to know how he got

his contact line to move.

All the best,

Paul

Randiburg2007-10-29 15:06:30

Thank you, Paul. Your help is appreciated.

Also, some interesting results at http://www.uni-stuttgart.de/itlr/engl/gallery/freesurf.html

True.

In fact, about VOF I have some image, especially about Los Alamos team’s

work, ie SOLA-VOF. I was interested in other approaches but I will stick

to this one I presume.

I will be away for the summer holiday. Also for you, have a nice summer

and take it easy

Randi B

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